The fans, in Rome for their side's Europa League game against Serie A side Lazio, were stabbed at different locations around the city, according to La Gazzetta dello Sport newspaper.
None of the injuries were life-threatening, according to the report.
Reuters reports a 50-year-old doctor was attacked at Ponte Milvio, a 30-year-old was stabbed nearby and a third was attacked outside the Hotel Hilton.
It is not the first time fans of Lazio are alleged to have to have been linked to acts of violence against visiting fans.
The Rome club has been targeted by European football's governing body UEFA after the Italians' Europa Cup tie with English Premier League side Tottenham was marred by racist chanting earlier this season.
Lazio were previously fined 40,200 euro by UEFA after monkey chants were directed at Tottenham players during the reverse fixture in London in September.